Finite Group Databasebeta

← #18006156

Subgroups — #18006156

Order 4736.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924569C211yesmaximal, characteristic, complemented
2C2×#11924558C211yesmaximal, characteristic, complemented
3#14558192C211yesmaximal, characteristic, complemented
4#14558188C211yesmaximal, characteristic, complemented
5#14557927C211yesmaximal, characteristic, complemented
6#14557779C211yesmaximal, characteristic, complemented
7#14557774C211yesmaximal, characteristic, complemented
8#14557749C211yesmaximal, characteristic, complemented
9#14557744C211yesmaximal, characteristic, complemented
10#14557697C211yesmaximal, characteristic, complemented
11#14557697C211yesmaximal, characteristic, complemented
12#14557691C211yesmaximal, characteristic, complemented
13#14557680C211yesmaximal, characteristic, complemented
14#14557635C211yesmaximal, characteristic, complemented
15C37×#435C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×#10596962C2211yescharacteristic
18C2×#10596962C2211yescharacteristic
19C22×Dic74C2211yescharacteristic
20#11924569—24no—
21#11924558—24no—
22C2×Dic148C2211yescharacteristic
23C2×Dic148C2211yescharacteristic
24C2×Dic148C2211yescharacteristic
25C2×Dic148C2211yescharacteristic
26C2×#10596930C2211yescharacteristic
27C2×#10596930C2211yescharacteristic
28C2×#10596930C2211yescharacteristic
29C2×#10596930C2211yescharacteristic
30C2×D296C2211yescharacteristic
31#11924536C2211yescharacteristic
32#11924524C2211yescharacteristic
33#11924522—21no—
34#11924518—21no—
35#11924518—21no—
36#11924515C2211yescharacteristic
37#11924515C2211yescharacteristic
38#11924515C2211yescharacteristic
39#11924514—21no—
40#11924510C2211yescharacteristic
41#11924508—21no—
42#11924507—21no—
43C4×Dic74C2211yescharacteristic
44C4×D148C2211yescharacteristic
45#11924496—21no—
46C4⋊C4×D37—21no—
47#11924470C2211yescharacteristic
48#11924461C2211yescharacteristic
49#11924461C2211yescharacteristic
50#11924461C2211yescharacteristic
51#11924461C2211yescharacteristic
52#11924458C2211yescharacteristic
53#11924458C2211yescharacteristic
54C2×M16×C37C2211yescharacteristic
55C22×C8×C37C2211yescharacteristic
56C4×D4×C37C2211yescharacteristic
57C4⋊C8×C37C2211yescharacteristic
58C22⋊C8×C37C2211yescharacteristic
59C22⋊C8×C37C2211yescharacteristic
60#97×C37C2211yescharacteristic
61C2×D4×C37D411yescharacteristic
62C22×C4×C37C2311yescharacteristic
63C22×C4×C37C2311yescharacteristic
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68C22×Dic37—21no—
69#10596962—22no—
70#10596962—22no—
71#10596962—22no—
72#10596962—41no—
73#10596962—41no—
74#10596962—41no—
75C2×D148C2311yescharacteristic
76C2×D148C2311yescharacteristic
77C2×C4×D37—21no—
78C2×C4×D37—21no—
79C2×C4×D37—21no—
80C2×C4×D37—21no—
81C2×Dic74—22no—
82C2×Dic74—21no—
83C2×Dic74—41no—
84C2×Dic74C2311yescharacteristic
85C2×Dic74C2311yescharacteristic
86C2×Dic74C2311yescharacteristic
87C2×Dic74C2311yescharacteristic
88M16×C37—22no—
89C2×C8×C37—22no—
90C2×C8×C37C2311yescharacteristic
91C2×C8×C37C2311yescharacteristic
92C2×C8×C37C2311yescharacteristic
93C2×C8×C37C2311yescharacteristic
94C4⋊C4×C37D411yescharacteristic
95C22⋊C4×C37D411yescharacteristic
96C22⋊C4×C37D411yescharacteristic
97C42×C37C2311yescharacteristic
98C22⋊Dic37—21no—
99C22⋊Dic37—21no—
100C22⋊Dic37—21no—
101#10596938—21no—
102#10596938—21no—
103#10596938—21no—
104#10596938—21no—
105C4⋊Dic37—21no—
106C4⋊Dic37—21no—
107C4⋊Dic37C2311yescharacteristic
108C4⋊Dic37C2311yescharacteristic
109#10596936—21no—
110#10596936—21no—
111#10596936—21no—
112#10596936—21no—
113C4×Dic37—21no—
114Dic148—22no—
115Dic148—22no—
116Dic148—22no—
117Dic148—41no—
118D296—22no—
119#10596930—22no—
120#10596930—22no—
121#10596930—41no—
122#10596930D414yescomplemented
123C23×C37C2×D411yescharacteristic
124C23×C37C2×D411yescharacteristic
125C22×D37—21no—
126C22×D37—21no—
127D4×C37—41no—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37C2×D411yescharacteristic
133C2×C4×C37C2×D411yescharacteristic
134C2×C4×C37C2×D411yescharacteristic
135C2×C4×C37C2×D411yescharacteristic
136C2×C4×C37C2411yescharacteristic
137C22⋊D37—42no—
138C22⋊D37—42no—
139C22⋊D37—42no—
140C22⋊D37—42no—
141C2×Dic37—21no—
142C2×Dic37—21no—
143C2×Dic37—21no—
144C2×Dic37—21no—
145C2×Dic37—21no—
146C2×Dic37—21no—
147C2×Dic37—42no—
148D148—21no—
149D148—21no—
150D148—21no—
151D148C2×D412yes—
152C4×D37—42no—
153C4×D37—42no—
154C4×D37—42no—
155C4×D37—42no—
156Dic74—21no—
157Dic74—21no—
158Dic74—21no—
159Dic74—21no—
160Dic74—21no—
161Dic74—21no—
162Dic74—21no—
163Dic74—42no—
164Dic74C2×D412yes—
165C8×C37—21no—
166C8×C37—21no—
167C8×C37—21no—
168C8×C37C2×D412yes—
169C22×C37—21no—
170C22×C37—21no—
171C22×C37—21no—
172C22×C37—21no—
173C22×C37—21no—
174C22×C37—21no—
175C22×C37C22×D411yescharacteristic
176C2×D37—22no—
177C2×D37—41no—
178C2×D37—41no—
179C2×D37—41no—
180C2×D37—41no—
181C2×D37—41no—
182C4×C37—21no—
183C4×C37—21no—
184C4×C37—21no—
185C4×C37—21no—
186C4×C37C22×D411yescharacteristic
187C4×C37H(5,𝔽2)11yescharacteristic
188Dic37—22no—
189Dic37—41no—
190Dic37—41no—
191Dic37—41no—
192Dic37—41no—
193Dic37—41no—
194#3269—371nomaximal, Sylow
195C2×C37—41no—
196C2×C37—41no—
197C2×C37D4211yescharacteristic
198C2×C37#57511yescharacteristic
199C2×C37#57811yescharacteristic
200D37—42no—
201D37—81no—
202C2×#137—371no—
203C2×#135—371no—
204#548—371no—
205#547—371no—
206#497—371no—
207#468—371no—
208#467—371no—
209#463—371no—
210#462—371no—
211#452—371no—
212#452—371no—
213#451—371no—
214#449—371no—
215#440—371no—
216#435D3711yescharacteristic, complemented
217C37#326911yescharacteristic, complemented, Sylow
218C2×#41—371no—
219C2×#41—371no—
220C2×#41—371no—
221C22×Q8—371no—
222#137—744no—
223#135—744no—
224C2×Q16—371no—
225C2×Q16—371no—
226C2×Q16—371no—
227C2×Q16—371no—
228C2×SD16—371no—
229C2×SD16—371no—
230C2×SD16—371no—
231C2×SD16—371no—
232C2×D8—371no—
233C2×M16C2×D3711yescharacteristic
234C22×C8C2×D3711yescharacteristic
235C4⋊Q8—371no—
236#124—371no—
237#124—741no—
238#123—741no—
239#123—741no—
240C22⋊Q8—371no—
241C22⋊Q8—371no—
242C22⋊Q8—371no—
243C22⋊Q8—741no—
244#121—371no—
245#121—741no—
246#121—741no—
247C4×Q8—371no—
248C4×D4—371no—
249C4×D4—741no—
250C4×D4C2×D3711yescharacteristic
251C2×C4⋊C4—741no—
252#107—371no—
253C4⋊C8C2×D3711yescharacteristic
254#103—371no—
255#103—371no—
256#103—371no—
257#103—371no—
258#102—371no—
259#102—371no—
260C22⋊C8C2×D3711yescharacteristic
261C22⋊C8C2×D3711yescharacteristic
262#97C2×D3711yescharacteristic
263#41—742no—
264#41—742no—
265#41—742no—
266#41—1481no—
267#41—1481no—
268#41—1481no—
269C2×Q8—371no—
270C2×Q8—371no—
271C2×Q8—371no—
272C2×Q8—371no—
273C2×Q8—742no—
274C2×Q8—741no—
275C2×Q8—1481no—
276C2×D4—371no—
277C2×D4—371no—
278C2×D4—741no—
279C2×D4—741no—
280C2×D4—741no—
281C2×D4—741no—
282C2×D4D14811yescharacteristic
283C22×C4—741no—
284C22×C4—741no—
285C22×C4—741no—
286C22×C4—741no—
287C22×C4—741no—
288C22×C4C22×D3711yescharacteristic
289C22×C4C22×D3711yescharacteristic
290Q16—742no—
291Q16—742no—
292Q16—742no—
293Q16—1481no—
294SD16—374no—
295SD16—742no—
296SD16—742no—
297SD16—1481no—
298D8—742no—
299M16—22no—
300C2×C8—22no—
301C2×C8C22×D3711yescharacteristic
302C2×C8C22×D3711yescharacteristic
303C2×C8C22×D3711yescharacteristic
304C2×C8C22×D3711yescharacteristic
305C4⋊C4—371no—
306C4⋊C4—371no—
307C4⋊C4—741no—
308C4⋊C4—741no—
309C4⋊C4—741no—
310C4⋊C4—741no—
311C4⋊C4—741no—
312C4⋊C4—741no—
313C4⋊C4D14811yescharacteristic
314C22⋊C4—741no—
315C22⋊C4—741no—
316C22⋊C4—741no—
317C22⋊C4—741no—
318C22⋊C4—741no—
319C22⋊C4—741no—
320C22⋊C4—741no—
321C22⋊C4D14811yescharacteristic
322C22⋊C4D14811yescharacteristic
323C42—741no—
324C42C22×D3711yescharacteristic
325C23—741no—
326C23—741no—
327C23C2×D14811yescharacteristic
328C23C2×D14811yescharacteristic
329Q8—372no—
330Q8—741no—
331Q8—741no—
332Q8—741no—
333Q8—741no—
334Q8—741no—
335Q8—741no—
336Q8—741no—
337Q8—1482no—
338D4—41no—
339D4—372no—
340D4—741no—
341D4—741no—
342D4—741no—
343D4—1482no—
344D4—1482no—
345D4—1482no—
346D4—1482no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—741no—
352C2×C4—741no—
353C2×C4—741no—
354C2×C4—741no—
355C2×C4—741no—
356C2×C4—741no—
357C2×C4—1482no—
358C2×C4—1482no—
359C2×C4—1482no—
360C2×C4—1482no—
361C2×C4—1482no—
362C2×C4C2×D14811yescharacteristic
363C2×C4C2×D14811yescharacteristic
364C2×C4C2×D14811yescharacteristic
365C2×C4C2×D14811yescharacteristic
366C2×C4C23×D3711yescharacteristic
367C8—21no—
368C8—21no—
369C8—21no—
370C8D4×D3712yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—742no—
378C22—1481no—
379C22—1481no—
380C22—1481no—
381C22—1481no—
382C22—1481no—
383C22C22×D14811yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—742no—
389C4—1481no—
390C4—1481no—
391C4—1481no—
392C4—1481no—
393C4—1481no—
394C4C2×D4×D3711yescharacteristic
395C4#1192458211yescharacteristic
396C2—41no—
397C2—41no—
398C2—2961no—
399C2—1482no—
400C2D4×D14811yescharacteristic
401C2#1455833311yescharacteristic
402C2#1455835011yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#435C2
socleC22×C37C22×D4
hypercenter#435D37
hypocenterC37#3269
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11924569C2semidirect
2. C2×#11924558C2semidirect
3. #14558192C2semidirect
4. #14558188C2semidirect
5. #14557927C2semidirect
6. #14557779C2semidirect
7. #14557774C2semidirect
8. #14557749C2semidirect
9. #14557744C2semidirect
10. #14557697C2semidirect
11. #14557697C2semidirect
12. #14557691C2semidirect
13. #14557680C2semidirect
14. #14557635C2semidirect
15. C37×#435C2semidirect
122. #10596930D4semidirect
216. #435D37semidirect
217. C37#3269semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#119245692
C2×#119245582
#145581922
#145581882
#145579272
#145577792
#145577742
#145577492
#145577442
#145576972
#145576912
#145576802
#145576352
C37×#4352
#326937